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| Type | Working Paper |
| Scope | Discipline-based scholarship |
| Title | Fictitious play in networks |
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| Authors |
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| Institution | University of Zurich |
| Series Name | Working paper series / Department of Economics |
| Number | 239 |
| ISSN | 1664-7041 |
| Number of Pages | 57 |
| Date | 2019 |
| Abstract Text | This paper studies fictitious play in networks of noncooperative two-person games. We show that continuous-time fictitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1/T, regardless of the size of the network. In contrast, arbitrary n-person zero-sum games with bilinear payoff functions do not possess the continuous-time fictitious-play property. As extensions, we consider networks in which each bilateral game is either strategically zero-sum, a weighted potential game, or a two-by-two game. In those cases, convergence requires a condition on bilateral payoffs or, alternatively, that the network is acyclic. Our results hold also for the discrete-time variant of fictitious play, which implies, in particular, a generalization of Robinson's theorem to arbitrary zero-sum networks. Applications include security games, conflict networks, and decentralized wireless channel selection. |
| Other Identification Number | merlin-id:14177 |
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| Keywords | Fictitious play, networks, zero-sum games, conflicts, potential games, Miyasawa's theorem, Robinson's theorem, Netzwerk, Nullsummenspiel, Konflikt, Konvergenz, Nichtkooperatives Spiel, Nash-Gleichgewicht, Netzwerk |
| Additional Information | Revised version |